A003618 Largest n-digit prime. (Formerly M4452)

7, 97, 997, 9973, 99991, 999983, 9999991, 99999989, 999999937, 9999999967, 99999999977, 999999999989, 9999999999971, 99999999999973, 999999999999989, 9999999999999937, 99999999999999997, 999999999999999989, 9999999999999999961, 99999999999999999989

Offset

1,1

Comments

Since 10^n - 1 is always a multiple of 9, one could be tempted to think that 9 is the least frequently occurring least significant digit in terms of this sequence. - Alonso del Arte, Dec 03 2017

The occurrences of least significant digits in the first 8000 terms (see A033874) are 1: 2028, 3: 2032, 7: 2014, and 9: 1926. - Giovanni Resta, Mar 16 2020

References

O'Hara, J. Rec. Math., 22 (1990), Table on page 278.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000 (terms 1..200 from T. D. Noe. Jon E. Schoenfield verified that terms 1..200 are indeed primes, Feb 02 2009)

Eric Weisstein's World of Mathematics, Previous Prime

R. G. Wilson, v., Extract from letter to N. J. A. Sloane, May 20 1994, with annotated scanned copy of page 278 of O'Hara article.

Example

No power of 10 is prime.
9 = 3^2, 8 = 2^3 but 7 is prime, so a(1) = 7.
99 = 3^2 * 11 but 97 is prime, so a(2) = 97.
999 = 3^3 * 37 but 997 is prime, so a(3) = 997.
9999 = 3^2 * 11 * 101, 9997 = 13 * 769, 9995 = 5 * 1999, 9993 = 3 * 3331, 9991 = 97 * 103, ..., 9975 = 5^2 * 399, but 9973 is prime, so a(4) = 9973.

Maple

a:= n-> prevprime(10^n):
seq(a(n), n=1..20);  # Alois P. Heinz, Feb 11 2021

Mathematica

NextPrime[10^Range[20], -1] (* Harvey P. Dale, Feb 03 2011 *)

Prog

(PARI) a(n)=precprime(10^n) \\ Charles R Greathouse IV, Jul 19 2011
(Magma) [PreviousPrime(10^n): n in [1..20]]; // Vincenzo Librandi, Sep 13 2016
(Python)
from sympy import prevprime
print([prevprime(10**n) for n in range(1, 21)]) # Michael S. Branicky, Feb 11 2021

Crossrefs

Cf. A003617, A033874, A114429 (largest n-digit twin prime).

Sequence in context: A125590 A068694 A158579 * A173833 A093172 A074110

Adjacent sequences: A003615 A003616 A003617 * A003619 A003620 A003621

Keyword

nonn,nice,base,changed

Author

N. J. A. Sloane, Mira Bernstein

Extensions

More terms from Stefan Steinerberger, Apr 08 2006

Status

approved